<s>
Probability	B-General_Concept
matching	I-General_Concept
is	O
a	O
decision	O
strategy	O
in	O
which	O
predictions	O
of	O
class	O
membership	O
are	O
proportional	O
to	O
the	O
class	O
base	O
rates	O
.	O
</s>
<s>
Thus	O
,	O
if	O
in	O
the	O
training	O
set	O
positive	O
examples	O
are	O
observed	O
60%	O
of	O
the	O
time	O
,	O
and	O
negative	O
examples	O
are	O
observed	O
40%	O
of	O
the	O
time	O
,	O
then	O
the	O
observer	O
using	O
a	O
probability-matching	B-General_Concept
strategy	O
will	O
predict	O
(	O
for	O
unlabeled	O
examples	O
)	O
a	O
class	O
label	O
of	O
"	O
positive	O
"	O
on	O
60%	O
of	O
instances	O
,	O
and	O
a	O
class	O
label	O
of	O
"	O
negative	O
"	O
on	O
40%	O
of	O
instances	O
.	O
</s>
<s>
The	O
optimal	O
Bayesian	B-General_Concept
decision	I-General_Concept
strategy	I-General_Concept
(	O
to	O
maximize	O
the	O
number	O
of	O
correct	O
predictions	O
,	O
see	O
)	O
in	O
such	O
a	O
case	O
is	O
to	O
always	O
predict	O
"	O
positive	O
"	O
(	O
i.e.	O
,	O
predict	O
the	O
majority	O
category	O
in	O
the	O
absence	O
of	O
other	O
information	O
)	O
,	O
which	O
has	O
60%	O
chance	O
of	O
winning	O
rather	O
than	O
matching	O
which	O
has	O
52%	O
of	O
winning	O
(	O
where	O
p	O
is	O
the	O
probability	O
of	O
positive	O
realization	O
,	O
the	O
result	O
of	O
matching	O
would	O
be	O
,	O
here	O
)	O
.	O
</s>
<s>
The	O
probability-matching	B-General_Concept
strategy	O
is	O
of	O
psychological	O
interest	O
because	O
it	O
is	O
frequently	O
employed	O
by	O
human	O
subjects	O
in	O
decision	O
and	O
classification	O
studies	O
(	O
where	O
it	O
may	O
be	O
related	O
to	O
Thompson	B-Algorithm
sampling	I-Algorithm
)	O
.	O
</s>
<s>
The	O
only	O
case	O
when	O
probability	B-General_Concept
matching	I-General_Concept
will	O
yield	O
same	O
results	O
as	O
Bayesian	B-General_Concept
decision	I-General_Concept
strategy	I-General_Concept
mentioned	O
above	O
is	O
when	O
all	O
class	O
base	O
rates	O
are	O
the	O
same	O
.	O
</s>
<s>
So	O
,	O
if	O
in	O
the	O
training	O
set	O
positive	O
examples	O
are	O
observed	O
50%	O
of	O
the	O
time	O
,	O
then	O
the	O
Bayesian	O
strategy	O
would	O
yield	O
50%	O
accuracy	O
(	O
1	O
×	O
.5	O
)	O
,	O
just	O
as	O
probability	B-General_Concept
matching	I-General_Concept
(	O
.5	O
×	O
.5	O
+	O
.5	O
×	O
.5	O
)	O
.	O
</s>
